This must be the oldest question . Any herbs that pests ( rabbits, deer, voles, etc ) don't tend to eat? Can't find a good list anywhere on the net.
Basil ? Parsley ? Oregeno ?
It really depends - deer will eat darn near anything when they're hungry enough. The culinary ones that I can grow outside the fence with few animal problems are oregano, chives, garlic, shallots (so far), sage and some of the standard mints. Another that would withstand browsing is horseradish though you really ahve to contain it. I haven't tried basil but parsley just hasn't worked without lots of browsing. I wonder if anyone has tried dill / anise?
If you're looking at more medicinals, there is a wider variety ... things like woodruff, yarrow, valerian, feverfew, goldenseal will do just fine.
I have to say its the one thing that I have not had any problems with - at least so far. I have oregano, rosemary, tarragon, sage, thyme and chives growing, and I plant basil every year. So far, the varmints have never touched them. I started up a small rock garden on a hill last year and planted some lemon thyme - it's huge by now, and nothing has ever touched it. Now bugs are a different matter, especially with the basil - something really likes that plant a lot.
I have heard that deer tend to avoid plants with scented leaves, but as has already been mentioned, they will eat just about anything if they are hungry emough. Maybe that's not as much a problem with the herbs in summer, when the deer have way too many other options :-) like my phlox !
Lavender seems to be fairly pest resistant. Deer have never snacked on mine. Also, sage, as the others stated. Deer have eaten my chives, leeks and shallots before, although most places say they don't like anything oniony. Maybe they had to eat all my leeks to be reminded of that! They also haven't eaten bee balm, mints or thymes.
Haven't had trouble with oregano, rosemary, thyme, tarragon, lovage or mints, but my deer LOVE the basil and parsley. Of course, you never know.
Was a little behind with spraying/fencing the shade garden this year, and the deer have destroyed it already. Hostas, goats beard, astilbes, even some of the ferns - gone. Ugh.
They munched on my decorative alliums this spring - first time for that and I suspect it was a fawn that didn't know any better because only a few leaves were eaten and the alliums went on to bloom. Out in the woods, spice bush or benzoin (lindera benzoin) is left strictly along - so much that it is the common understory shrub since the deer have eaten all its competition. They haven't touched any of the wormwoods and they won't eat digitalis though they have munched on hellbores and monkshood - both poisonous! I hope they had at least a stomach ache. They don't eat lily of the valley either.
Have to say that life is a lot easier since the deer fence went up.
Don't be so sure about lily of the valley...same shade garden as post above, mine munched this year along with the Solomon's seal and everything else. Hostas are making a comeback though thankfully. Definately deer - tracks are all over.